City investors in Lloyds Banking Group are warning that it should not hand its chief executive a substantial bonus for 2011 after a sharp slump in its share price as well as his two month-absence for fatigue.I've spoken to several major Lloyds shareholders in the last 24 hours who welcome the fact that Antonio Horta-Osorio will be returning to his job next month yet who believe that his temporary departure should be reflected in his annual compensation award.Horta-Osorio is contractually entitled to a bonus of approximately £2.4m, or 225 per cent of his base salary of £1.061m.Underlining increasingly intense shareholder concerns about bankers' pay, some investors believe a seven-figure bonus for the Lloyds boss would be "inappropriate" despite the zeal with which he has attacked a string of legacy issues at the bank.The big shareholders who have expressed a view to me about Horta-Osorio's 2011 pay don't include UK Financial Investments, the body which manages taxpayers' 41 per cent stake in the bank.Robert Talbut, chief investment officer at Royal London Asset Management, said: "Any outcome for executive directors has to reflect the returns that shareholders are receiving."Given that Lloyds is unable to pay a dividend for another year (under the terms of its bail-out by taxpayers), and the fact that the bank's share price has tumbled since Horta-Osorio took over in March, being a Lloyds shareholder has been a miserable experience in 2011.In an interview I've just done with him, Horta-Osorio declined to comment on investors' comments about his bonus entitlement, although to be clear, the subject of his annual pay award will not be formally discussed by Lloyds' remuneration committee for several weeks.Following Lloyds' announcement yesterday that he would return to work on January 9, Horta-Osorio said he was certain he was well enough to return but admitted that he had had to sleep under medical supervision."I'm feeling very well, I am sleeping much better. I got very close to my battery going to zero. I started to suffer [from sleep deprivation] at the beginning of September and by the end of October I could not sleep at all," he told me."I went to see [Sir] Win [Bischoff, Lloyds' chairman] on October 31st and said it was not working and that I had to see a specialist."Horta-Osorio said he was confident that he would not suffer a relapse."I will be mindful of any early warning signals and if they did occur I would consult doctors immediately. I will be restructuring my management team and reducing my number of direct reports. It would be normal to do that and delegate more in the second phase of our turnaround plan."But he insisted that he would not appoint a deputy or a chief operating officer."I didn't do that at Santander UK and I don't think it would be appropriate here," he said.Horta-Osorio attributed his fatigue to the urgency with which he approached the job when he arrived early in the year."I had to get stuck into a number of priorities in March, some of which were not delegateable: the fact that I had to hire several senior people, the PPI [payment protection insurance] provision, my strategic review, and repaying the SLS [special liquidity scheme] ahead of schedule. I had to do them quickly because I was concerned that we were about to go into much worse economic situation. That's why I had a sense of urgency."Yet he acknowledges that times have not got any easier since his enforced departure."The Eurozone situation is clearly deteriorating, and given that 40 per cent of the UK's exports go to Europe, it has to have an effect. But I know the responsibility I have and I do not take it lightly. I'm determined that Lloyds supports the UK economy and that we help the Treasury get taxpayers' money back."Separately, Lloyds has just confirmed my story that Horta-Osorio is aiming to demonstrate his confidence in the bank's future by acquiring another 600,000 Lloyds shares.Right now, the roadblocks ahead look sufficiently challenging that even where the shares currently languish, it's a bold vote for a turnaround of Lloyds' fortunes.